Offprint · The e Supplement · Supplement 2.71

Rise

Half full, one doubling before the top.

A starter that doubles every four hours grows by the same small fraction every minute of those four hours. Growth that feeds on itself is written with e.

Left a day, it would double six times and be sixty-four times its size, if the jar allowed.

The jar is half full one doubling before it overflows. Most of the rising happens at the end.

×1×2×4×8×16×32×64

After 12 hours, doubling every 4: 8.00 times the start. Written with e, that is e to the 0.173 per hour.

Figure Each gridline is one more doubling. On this scale, steady doubling is a straight line.

“Rise.” The e Supplement, supplement 2.71 (24 September 2026). wap.mom/rise/